I'm at a similar point. I have about one years worth of savings in the bank and could probably stretch it to two years if I sell some stocks. I'm also young so if I blow through that money I will recover.
A friend of mine had a great idea that we are going to work on and I just thought it's now or never. If I try to work and do this on the side, I don't really see myself putting in as much as I could and it would be a regret down the road.
The "To quit or not to quit" question isn't so black and white. Definitely don't quit if you are living paycheck-to-paycheck but if you have at least a year's worth of living expenses saved up, I think it's worth it to give it a shot.
Yes, some people build businesses while they are working full-time. Other people need the motivation or time of giving it their all. It's a case-by-case scenario.